The first results on K⁎(892)± resonance production in inelastic pp collisions at LHC energies of s=5.02, 8, and 13 TeV are presented. The K⁎(892)± has been reconstructed via its hadronic decay channel K⁎(892)→±KS0+π± with the ALICE detector. Measurements of transverse momentum distributions, pT-integrated yields, and mean transverse momenta for charged K⁎(892) are found to be consistent with previous ALICE measurements for neutral K⁎(892) within uncertainties. For pT>1 GeV/c the K⁎(892)± transverse momentum spectra become harder with increasing centre-of-mass energy from 5.02 to 13 TeV, similar to what previously observed for charged kaons and pions. For pT<1 GeV/c the K⁎(892)± yield does not evolve significantly and the abundance of K⁎(892)± relative to K is rather independent of the collision energy. The transverse momentum spectra, measured for K⁎(892)± at midrapidity in the interval 0 < pT<15 GeV/c, are not well described by predictions of different versions of PYTHIA 6, PYTHIA 8 and EPOS-LHC event generators. These generators reproduce the measured pT-integrated K⁎±/K ratios and describe well the momentum dependence for pT<2 GeV/c.